Problem: Solve for $x$ and $y$ using elimination. ${5x-2y = 25}$ ${-3x+2y = -11}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $2x = 14$ $\dfrac{2x}{{2}} = \dfrac{14}{{2}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {5x-2y = 25}\thinspace$ to find $y$ ${5}{(7)}{ - 2y = 25}$ $35-2y = 25$ $35{-35} - 2y = 25{-35}$ $-2y = -10$ $\dfrac{-2y}{{-2}} = \dfrac{-10}{{-2}}$ ${y = 5}$ You can also plug ${x = 7}$ into $\thinspace {-3x+2y = -11}\thinspace$ and get the same answer for $y$ : ${-3}{(7)}{ + 2y = -11}$ ${y = 5}$